IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v220y2009i7p1034-1042.html
   My bibliography  Save this article

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

Author

Listed:
  • Schimit, P.H.T.
  • Monteiro, L.H.A.

Abstract

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R0) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R0 cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations.

Suggested Citation

  • Schimit, P.H.T. & Monteiro, L.H.A., 2009. "On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata," Ecological Modelling, Elsevier, vol. 220(7), pages 1034-1042.
    • Handle: RePEc:eee:ecomod:v:220:y:2009:i:7:p:1034-1042
    DOI: 10.1016/j.ecolmodel.2009.01.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380009000386
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2009.01.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kleczkowski, Adam & Grenfell, Bryan T., 1999. "Mean-field-type equations for spread of epidemics: the ‘small world’ model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 355-360.
    2. Monteiro, L.H.A. & Sasso, J.B. & Chaui Berlinck, J.G., 2007. "Continuous and discrete approaches to the epidemiology of viral spreading in populations taking into account the delay of incubation time," Ecological Modelling, Elsevier, vol. 201(3), pages 553-557.
    3. Zhang, Zhibin, 2007. "The outbreak pattern of SARS cases in China as revealed by a mathematical model," Ecological Modelling, Elsevier, vol. 204(3), pages 420-426.
    4. Fuentes, M.A. & Kuperman, M.N., 1999. "Cellular automata and epidemiological models with spatial dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 267(3), pages 471-486.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pereira, F.M.M. & Schimit, P.H.T., 2018. "Dengue fever spreading based on probabilistic cellular automata with two lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 75-87.
    2. Schimit, P.H.T. & Monteiro, L.H.A., 2012. "On estimating the basic reproduction number in distinct stages of a contagious disease spreading," Ecological Modelling, Elsevier, vol. 240(C), pages 156-160.
    3. Jianhong Chen & Hongcai Ma & Shan Yang, 2023. "SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    4. Schimit, P.H.T. & Monteiro, L.H.A., 2011. "A vaccination game based on public health actions and personal decisions," Ecological Modelling, Elsevier, vol. 222(9), pages 1651-1655.
    5. Chuangxia Huang & Jie Cao & Fenghua Wen & Xiaoguang Yang, 2016. "Stability Analysis of SIR Model with Distributed Delay on Complex Networks," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-22, August.
    6. Schimit, P.H.T. & Monteiro, L.H.A., 2010. "Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases," Ecological Modelling, Elsevier, vol. 221(9), pages 1329-1332.
    7. Ramos, A.B.M. & Schimit, P.H.T., 2019. "Disease spreading on populations structured by groups," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 265-273.
    8. Schimit, P.H.T., 2016. "Evolutionary aspects of spatial Prisoner’s Dilemma in a population modeled by continuous probabilistic cellular automata and genetic algorithm," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 178-188.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Schimit, P.H.T. & Monteiro, L.H.A., 2012. "On estimating the basic reproduction number in distinct stages of a contagious disease spreading," Ecological Modelling, Elsevier, vol. 240(C), pages 156-160.
    2. Schimit, P.H.T. & Monteiro, L.H.A., 2010. "Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases," Ecological Modelling, Elsevier, vol. 221(9), pages 1329-1332.
    3. Frank H. Koch & Denys Yemshanov & Daniel W. McKenney & William D. Smith, 2009. "Evaluating Critical Uncertainty Thresholds in a Spatial Model of Forest Pest Invasion Risk," Risk Analysis, John Wiley & Sons, vol. 29(9), pages 1227-1241, September.
    4. Mugnaine, Michele & Gabrick, Enrique C. & Protachevicz, Paulo R. & Iarosz, Kelly C. & de Souza, Silvio L.T. & Almeida, Alexandre C.L. & Batista, Antonio M. & Caldas, Iberê L. & Szezech Jr, José D. & V, 2022. "Control attenuation and temporary immunity in a cellular automata SEIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    5. Chen Renbao & Wang Ping, 2008. "Modeling the Cumulative Cases from SARS," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 2(2), pages 1-17, March.
    6. Xiao, Yao & Yang, Mofeng & Zhu, Zheng & Yang, Hai & Zhang, Lei & Ghader, Sepehr, 2021. "Modeling indoor-level non-pharmaceutical interventions during the COVID-19 pandemic: A pedestrian dynamics-based microscopic simulation approach," Transport Policy, Elsevier, vol. 109(C), pages 12-23.
    7. Mattia Mazzoli & Riccardo Gallotti & Filippo Privitera & Pere Colet & José J. Ramasco, 2023. "Spatial immunization to abate disease spreading in transportation hubs," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    8. Pereira, F.M.M. & Schimit, P.H.T., 2018. "Dengue fever spreading based on probabilistic cellular automata with two lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 75-87.
    9. Xu Zhao & Hengxing Xiang & Feifei Zhao, 2023. "Measurement and Spatial Differentiation of Farmers’ Livelihood Resilience Under the COVID-19 Epidemic Outbreak in Rural China," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 166(2), pages 239-267, April.
    10. Fatima-Zohra Younsi & Ahmed Bounnekar & Djamila Hamdadou & Omar Boussaid, 2019. "Integration of Multiple Regression Model in an Epidemiological Decision Support System," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1755-1783, November.
    11. Monteiro, L.H.A. & Sasso, J.B. & Chaui Berlinck, J.G., 2007. "Continuous and discrete approaches to the epidemiology of viral spreading in populations taking into account the delay of incubation time," Ecological Modelling, Elsevier, vol. 201(3), pages 553-557.
    12. Saoud, Bilal & Moussaoui, Abdelouahab, 2018. "A new hierarchical method to find community structure in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 418-426.
    13. Ramos, A.B.M. & Schimit, P.H.T., 2019. "Disease spreading on populations structured by groups," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 265-273.
    14. Diego R. Amancio & Osvaldo N. Oliveira jr & Luciano F. Costa, 2015. "Topological-collaborative approach for disambiguating authors’ names in collaborative networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 102(1), pages 465-485, January.
    15. Mark C. Andersen & Heather Adams & Bruce Hope & Mark Powell, 2004. "Risk Analysis for Invasive Species: General Framework and Research Needs," Risk Analysis, John Wiley & Sons, vol. 24(4), pages 893-900, August.
    16. Lu Tang & Yiwang Zhou & Lili Wang & Soumik Purkayastha & Leyao Zhang & Jie He & Fei Wang & Peter X.‐K. Song, 2020. "A Review of Multi‐Compartment Infectious Disease Models," International Statistical Review, International Statistical Institute, vol. 88(2), pages 462-513, August.
    17. Yang, Yang & Sun, Peng Gang & Hu, Xia & Li, Zhou Jun, 2014. "Closed walks for community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 129-143.
    18. Huiyu Xuan & Lida Xu & Lu Li, 2009. "A CA-based epidemic model for HIV/AIDS transmission with heterogeneity," Annals of Operations Research, Springer, vol. 168(1), pages 81-99, April.
    19. Ronald N. Kostoff & Stephen A. Morse, 2011. "Structure and infrastructure of infectious agent research literature: SARS," Scientometrics, Springer;Akadémiai Kiadó, vol. 86(1), pages 195-209, January.
    20. Ilnytskyi, Jaroslav & Kozitsky, Yuri & Ilnytskyi, Hryhoriy & Haiduchok, Olena, 2016. "Stationary states and spatial patterning in an SIS epidemiology model with implicit mobility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 36-45.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecomod:v:220:y:2009:i:7:p:1034-1042. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.